The fixed points of holomorphic maps on a convex domain

Volume 56 / 1992

Thai Do Annales Polonici Mathematici 56 (1992), 143-148 DOI: 10.4064/ap-56-2-143-148


We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in $ℂ^n$ then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.


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